Maybe if you went with a smaller flock, therefore less pallets needed, they would be willing to pick up pallets. Or maybe you have a friend who could help.
I see you want bantams. They require less room. A bantam coop needsat least 2 square feet of coop space and 5 square feet of run space (double that for large hens).
Pallets are roughly 4X4, enough floor space for 2 bantys. 2 pallets joined could be used for 4 bantys. Two long walls will each need 2 pallets while the two end walls only need 1. So far that is 8 pallets. You could make that 7 pallets by leaving one off of a long side and building a large clean-out door. The roof should be plywood.
There is also the cattle panel hoop house method. You might be able to buy a used panel somewhere. They're originally about $25 and about 4ft 2in wide by 16ft long. 2 of them covered with hardware cloth and heavy tarps and build a door on the one end, a wall on the other, you've got a 4x8 coop. Add 5 more panels minus the tarps for a run. A bit more money wise but very easy to build.
I hope you can find someone to help you gather your materials whatever you choose.
